Studies have shown that there is a strong relationship between sleep disordered breathing (SDB) and dementia and patients with Alzheimer's Disease having a high rate of SDB. This application will examine whether treating SDB with nasal CPAP in patients with AD will result in improvement in cognitive functioning. The specific aims are to assess whether patients with mild AD will tolerate CPAP and be compliant with the treatment; to examine the effect of CPAP treatment on SDB; to examine the effects of CPAP treatment on cognitive functioning in patients with mild AD and SDB; to examine whether improvement is greater after 6 weeks of CPAP treatment than after 3 weeks. Because caregivers are often disturbed by the patient's poor sleep, the effect of treatment on the caregiver will also be evaluated. The secondary aim is to evaluate whether caregivers feel that their own sleep improves as the patient's sleep improves. Patients will be randomized to a CPAP treatment group or sham CPAP group. After 3 weeks, the sham group will also be switched to CPAP. Measures of neuropsychological performance will be obtained at baseline and after 3 and 6 weeks of treatment.